I’ve been wondering this (transgender ‘rights’ vs religious freedom) as the yoga studio I go to have recently started an Ummah Yoga women-only class, with Muslim women in mind, but open to women of any faiths and none. The listing doesn’t specify how they are defining woman, and you’d hope that any decent male-bodied person would not seek to impose themselves upon Muslim women needing a single sex space to exercise in, however they (the male-bodied person) viewed their own gender identity. But I do fear that someone may try to take advantage. It’s a very multicultural historically working class area undergoing gentrification rapidly.
As I’m neither Muslim nor transgender, it’s not my personal issue, but I really hope that the studio are ready to invoke the EA exceptions to maintain a single-sex space should they be challenged.